| Title:
|
On sequential properties of Banach spaces, spaces of measures and densities (English) |
| Author:
|
Borodulin-Nadzieja, Piotr |
| Author:
|
Plebanek, Grzegorz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
381-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that a conjunction of Mazur and Gelfand-Phillips properties of a Banach space $E$ can be naturally expressed in terms of {\it weak}* continuity of seminorms on the unit ball of $E^*$. \endgraf We attempt to carry out a construction of a Banach space of the form $C(K)$ which has the Mazur property but does not have the Gelfand-Phillips property. For this purpose we analyze the compact spaces on which all regular measures lie in the {\it weak}* sequential closure of atomic measures, and the set-theoretic properties of generalized densities on the natural numbers. (English) |
| Keyword:
|
Gelfand-Phillips property |
| Keyword:
|
Mazur property |
| Keyword:
|
generalized density |
| MSC:
|
46B26 |
| MSC:
|
46E15 |
| MSC:
|
46E27 |
| idZBL:
|
Zbl 1224.46031 |
| idMR:
|
MR2657956 |
| . |
| Date available:
|
2010-07-20T16:46:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140576 |
| . |
| Reference:
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